Gravitational Doppler

Sci astro added, sci.math and comp.ai.p.. removed.


Lester Zick wrote:
On 24 Jul 2006 09:11:21 -0700, wrote:


Lester Zick wrote:
Gravitational Doppler
~v~~

We are well aware of gravitational lensing but there is another EM
analog associated with Newtonian universal gravitation as well:
gravitational doppler. In other words with latency extensions to
Newtonian universal gravitation we can explain planetary orbital
perihelion anomalies and calculate the Pioneer anomaly in simple,
direct terms.

To do this we only need to calculate Pioneer's velocity away from the
sun as a fraction of the speed of light and recognize that the effect
of the sun's gravitation will increase in proportion:

(Numbers used here were drawn from a column 1 article in the L. A.
Times of 12/21/2004 and are not exact)

Yearly distance traveled by Pioneer = 219,000,000 miles

Yearly discrepancy in distance = 8,000 miles

Ratio = ~ 27,375

speed of light = 186,289 miles per
second

Yearly distance traveled by light in one year=

186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr

Divided by yearly distance traveled by Pioneer

Ratio = ~ 26,825

A difference between the two ratios of 2% (27375 - 26,825 / 27,375)

QED

~v~~

I can't see any relation between the calculation above
and the description below.

Perhaps it wasn't as clear as I had hoped.

I made an error in my calculation, I used km/s
in one place and m/s in another, doh! That
knocks a factor of 1000 out in the results so
our numbers are much closer, sorry.

At the time of publication
Pioneer was traveling about 7 miles/sec (actually 6.9444 . . .
according to my calculation.

In January 1987 the speed was 7.984026 mile/sec
In December 1994 the speed was 7.706486 mile/sec

That number in relation to the speed of
light produces a ratio around 27,000

The ratios above are 23332 and 24172 respectively so
that's not bad given that you are using approximate
speeds.

or within 2% of the discrepancy
in distance traveled. In other words the discrepancy in expected
yearly distance of travel would be proportional to the ratio between
the speed of travel and the speed of light taken as the speed of
propagation for gravity.

Now that's where we diverge. What do you mean
by "the discrepancy in expected yearly distance
of travel"? The anomaly is a constant acceleration
so the discrepancy is speed increases each year
and the discrepancy in distance is quadratic.

Ordinarily we consider doppler primarily in terms of repulsive forces,
radiation, sound, etc.

No, ordinarily we think of Doppler as a change of
frequency and not related to forces. Light is an
exception since radiation pressure depends on
frequency, but that's not too significant at the
moment

However doppler also operates in analogous
terms for attractive forces such as gravitation, electrostatic, and
magnetic forces except that effects are reversed.

Consider two strong magnets on a table. They remain stationary as long
as first order friction effects exceed magnetic attraction between
them. However if one magnet is dragged away from the other at high
speed the other magnet experiences an excess force of attraction
causing it to move toward the moving magnet.

Really? I haven't worked out the details but I
haven't seen that effect. I suppose it might
result from induction.

The effect is pure doppler except in the case of attractive forces an
increase in speed away increases wavelengths and strength of the
attractive force. The same is true of all attractive forces operating
through space. Increasing wavelengths of attractive forces increases
the degree of attraction and decreasing wavelengths of attractive
forces decreases attraction by amounts proportional to increases or
decreases of speed in relation to the speed of propagation for the
force, the speed of light.

Imagine for a moment that the locus of attraction in the solar system
suddenly moves. Do you imagine that planetary orbits would be
unaffected?

Changes in gravity are expected to propagate at c.

If the sun suddenly moved away from the earth the earth
would be tugged toward it by an amount linearly related to the speed
of movement of the sun and having nothing to do with gravitational
constants.

No, it would be unaffected for about 500s then the
force would start to diminish. I don't think you are
talking of gravito-magnetic effects which would be
very small if they existed in that configuration.

And conversely if the sun suddenly moved toward the earth
its attraction would be lessened by a comparable amount and the orbit
of the earth extended as a result.

Now in approaching the Pioneer anomaly all I did was show that the
ratio between distance of expected travel and discrepancy in expected
travel were almost identical (witnin 2%) of the speed of travel and
the speed of light. I extrapolated the magnitudes over a year to
conserve precision. In other words if we call the expected distance of
travel D and the discrepancy in expected travel d, the speed of travel
v and the speed of light c we find that D/d is almost exactly c/v.

The problem there is that the discrepancy is a constant
acceleration a_P hence

d = 1/2 * a_P * t^2

while the speed is almost constant so

D ~ v * t

then

D/d ~ (2 * v) / (a_P * t)

snip Mercury

I hope this explanation is a little clearer.

Yes, it is better and hopefully my consternation is
a little clearer too. v/c is constant and D increases
linearly with time whereas d increases with the
square of time because it is a constant acceleration.

In other words Pioneer travels about 7 miles per second away from the
sun and in doing so gravitation waves lengthen and their attractive
intensity is experienced longer in each wave. (In this respect unlike
repulsive waves like EM radiation, the effect of attraction increases
in gravitation with longer waves and decreases with shorter waves.)
And conversely the attraction of gravitation should decrease as the
sun is approached.

If it is increased when the craft is moving away from
the Sun and decreased when moving towards, it is
first order and the Sun's gravitational effect would be
changed from

a = GM/r^2

to

a' = (1+v/c) * GM/r^2

The discrepancy would be

a_P = v/c * GM/r^2

For Pioneer 10 that varies from 1.58*10^-13 m/s^2 at
40AU down to 6.77*10^-14 m/s^2 at 60AU. The anomaly
is actually 8.74*10^-10 m/s^2 so your prediction is too
small by a factor of about 5000 at the start and more than
double that by the end of the period they studied. Your

Clearly the Pioneer Anomaly is caused by what I call gravitational
doppler. ....

Not even close.

Well, George, I'm not sure what the problem is here.

Most of it was mine.

I show the
expected discrepancy in distance traveled by Pioneer is proportional
to c/v and you tell me it isn't because you insist on relating it to
gravitational acceleration instead of the actual anomaly. The
discrepancy is in net distance traveled versus expected distance
traveled and not in gravitational acceleration.

I was trying to understand your description and guessed
badly. You said the extra force was related to the speed
ratio and since that is dimensionless you need to multiply
it by an acceleration or speed to get it into dynamical units.

The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.

I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

George

On 24 Jul 2006 13:51:41 -0700, wrote:

Sci astro added, sci.math and comp.ai.p.. removed.


Lester Zick wrote:
On 24 Jul 2006 09:11:21 -0700, wrote:


Lester Zick wrote:
Gravitational Doppler
~v~~

We are well aware of gravitational lensing but there is another EM
analog associated with Newtonian universal gravitation as well:
gravitational doppler. In other words with latency extensions to
Newtonian universal gravitation we can explain planetary orbital
perihelion anomalies and calculate the Pioneer anomaly in simple,
direct terms.

To do this we only need to calculate Pioneer's velocity away from the
sun as a fraction of the speed of light and recognize that the effect
of the sun's gravitation will increase in proportion:

(Numbers used here were drawn from a column 1 article in the L. A.
Times of 12/21/2004 and are not exact)

Yearly distance traveled by Pioneer = 219,000,000 miles

Yearly discrepancy in distance = 8,000 miles

Ratio = ~ 27,375

speed of light = 186,289 miles per
second

Yearly distance traveled by light in one year=

186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr

Divided by yearly distance traveled by Pioneer

Ratio = ~ 26,825

A difference between the two ratios of 2% (27375 - 26,825 / 27,375)

QED

~v~~

I can't see any relation between the calculation above
and the description below.

Perhaps it wasn't as clear as I had hoped.

I made an error in my calculation, I used km/s
in one place and m/s in another, doh! That
knocks a factor of 1000 out in the results so
our numbers are much closer, sorry.

No problem. A corrected error is not an error in my book.

At the time of publication
Pioneer was traveling about 7 miles/sec (actually 6.9444 . . .
according to my calculation.

In January 1987 the speed was 7.984026 mile/sec
In December 1994 the speed was 7.706486 mile/sec

Interesting. The article was dated 12/21/04 so my calculation of v
seems right in line.

That number in relation to the speed of
light produces a ratio around 27,000

The ratios above are 23332 and 24172 respectively so
that's not bad given that you are using approximate
speeds.

Yeah. But I think you have to realize that I wasn't using speeds
directly as there were no speeds indicated in the article (alas!). All
I had to go on were the yearly expectation of distance D for some year
and the yearly discrepancy d presumably for the same year. So what I
did was multiply out the distance covered by light in one year and use
that in relation to D and d instead of velocities. So even assuming
the distances were approximate and for the same year and little or no
significant deceleration occured I think we can only infer that my
calculations are accurate.

or within 2% of the discrepancy
in distance traveled. In other words the discrepancy in expected
yearly distance of travel would be proportional to the ratio between
the speed of travel and the speed of light taken as the speed of
propagation for gravity.

Now that's where we diverge. What do you mean
by "the discrepancy in expected yearly distance
of travel"?

That's roughly the way the numbers were described in the article. As
noted just above I didn't use velocity numbers directly but expected
distance D and discrepancy in distance d in one year's travel because
that's what the article gave.

The anomaly is a constant acceleration
so the discrepancy is speed increases each year
and the discrepancy in distance is quadratic.

Disagree. Especially at distances where little or no significant
acceleration occurs.

Ordinarily we consider doppler primarily in terms of repulsive forces,
radiation, sound, etc.

No, ordinarily we think of Doppler as a change of
frequency and not related to forces. Light is an
exception since radiation pressure depends on
frequency, but that's not too significant at the
moment

Oh I expect sonic doppler entails a repulsive force too.

However doppler also operates in analogous
terms for attractive forces such as gravitation, electrostatic, and
magnetic forces except that effects are reversed.

Consider two strong magnets on a table. They remain stationary as long
as first order friction effects exceed magnetic attraction between
them. However if one magnet is dragged away from the other at high
speed the other magnet experiences an excess force of attraction
causing it to move toward the moving magnet.

Really? I haven't worked out the details but I
haven't seen that effect. I suppose it might
result from induction.

I have actually done it and while I expect there are different ways to
describe the same mechanics the easiest is doppler especially when we
consider the effect on planetary orbits of anomalous motion of the
sun. If we try to explain both effects on a common basis then doppler
seems to be the only way to go.

The effect is pure doppler except in the case of attractive forces an
increase in speed away increases wavelengths and strength of the
attractive force. The same is true of all attractive forces operating
through space. Increasing wavelengths of attractive forces increases
the degree of attraction and decreasing wavelengths of attractive
forces decreases attraction by amounts proportional to increases or
decreases of speed in relation to the speed of propagation for the
force, the speed of light.

Imagine for a moment that the locus of attraction in the solar system
suddenly moves. Do you imagine that planetary orbits would be
unaffected?

Changes in gravity are expected to propagate at c.

Of course. And I have no doubt the basic force itself does too. At
least that's what I would infer from my calculation of the Pioneer
anomaly as well as the idea that gravitation propagates in waves.

If the sun suddenly moved away from the earth the earth
would be tugged toward it by an amount linearly related to the speed
of movement of the sun and having nothing to do with gravitational
constants.

No, it would be unaffected for about 500s then the
force would start to diminish. I don't think you are
talking of gravito-magnetic effects which would be
very small if they existed in that configuration.

Well of course there is the propagation delay to consider but the
effect itself would still occur. But whether you're talking attraction
increase or decrease would depend on the direction of motion.

And conversely if the sun suddenly moved toward the earth
its attraction would be lessened by a comparable amount and the orbit
of the earth extended as a result.

Now in approaching the Pioneer anomaly all I did was show that the
ratio between distance of expected travel and discrepancy in expected
travel were almost identical (witnin 2%) of the speed of travel and
the speed of light. I extrapolated the magnitudes over a year to
conserve precision. In other words if we call the expected distance of
travel D and the discrepancy in expected travel d, the speed of travel
v and the speed of light c we find that D/d is almost exactly c/v.

The problem there is that the discrepancy is a constant
acceleration a_P hence

d = 1/2 * a_P * t^2

And I strongly (but politely) disagree because the anomaly is between
actual distance traveled versus expected distance traveled. Everything
else represents potential assumptions and interpretations used to
explain the source of discrepancy but the actual discrepancy itself is
actual distance traveled versus expected distance traveled.

while the speed is almost constant so

D ~ v * t

then

D/d ~ (2 * v) / (a_P * t)

snip Mercury

I hope this explanation is a little clearer.

Yes, it is better and hopefully my consternation is
a little clearer too. v/c is constant and D increases
linearly with time whereas d increases with the
square of time because it is a constant acceleration.

In the absence of significant acceleration v/c is constant and both D
and d are linear functions of time and constant over one year periods.

In other words Pioneer travels about 7 miles per second away from the
sun and in doing so gravitation waves lengthen and their attractive
intensity is experienced longer in each wave. (In this respect unlike
repulsive waves like EM radiation, the effect of attraction increases
in gravitation with longer waves and decreases with shorter waves.)
And conversely the attraction of gravitation should decrease as the
sun is approached.

If it is increased when the craft is moving away from
the Sun and decreased when moving towards, it is
first order and the Sun's gravitational effect would be
changed from

a = GM/r^2

to

a' = (1+v/c) * GM/r^2

The discrepancy would be

a_P = v/c * GM/r^2

For Pioneer 10 that varies from 1.58*10^-13 m/s^2 at
40AU down to 6.77*10^-14 m/s^2 at 60AU. The anomaly
is actually 8.74*10^-10 m/s^2 so your prediction is too
small by a factor of about 5000 at the start and more than
double that by the end of the period they studied. Your

Clearly the Pioneer Anomaly is caused by what I call gravitational
doppler. ....

Not even close.

Well, George, I'm not sure what the problem is here.

Most of it was mine.

Not a problem.

I show the
expected discrepancy in distance traveled by Pioneer is proportional
to c/v and you tell me it isn't because you insist on relating it to
gravitational acceleration instead of the actual anomaly. The
discrepancy is in net distance traveled versus expected distance
traveled and not in gravitational acceleration.

I was trying to understand your description and guessed
badly. You said the extra force was related to the speed
ratio and since that is dimensionless you need to multiply
it by an acceleration or speed to get it into dynamical units.

Well you know I'd like to stay away from the term "force" in the
present context because I can't describe how this force translates
into a constant change in velocity at present. All I can actually
claim is to have calculated a constant ratio v/c reflective of the
anomaly to within 2% and speculate it is a linear doppler ratio
indicating a relative lenghening in gravitational wavelenghts.

The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.

I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

All I have right now is a linear ratio v/c which correlates with the
Pioneer anomaly almost exactly. The ratio almost certainly reflects a
first order doppler effect in terms of the propagation of gravitation
but exactly how this ratio translates into a constant change in v is
not apparent at least to me. Perhaps there are others more familiar
with longitudinal doppler effects who could comment. However it is
enough for the present that we can calculate the effect directly. As
noted in a collateral post I never suggested I can calculate variances
in gravitational constants directly as a function of velocity. But I'm
convinced the effect itself is real and the calculations reflect that.

Lester Zick
~v~~

I'll coalesce my replies:


"Lester Zick" wrote in message
...
On Mon, 24 Jul 2006 22:38:04 +0100, "George Dishman"
wrote:
"Lester Zick" wrote in message
. ..
On 24 Jul 2006 05:20:36 -0700, wrote:
....

Lester, the original Anderson paper is he

http://www.arxiv.org/abs/gr-qc/0104064

That's the abstract, there should be a PDF option
on the page that gives you the full document (I have
some preferences set so I get PDF by default, it
might be an option for you).

I haven't seen the article but you said "Yearly
discrepancy in distance = 8,000 miles" so in 8
years that means a total of 64,000 miles, doesn't
it? Anyway my point is that there isn't a consistent
value for "yearly discrepancy in distance" it is
different every year.

Sure there would be with any acceleration. My point here is that
Pioneer is so far out that acceleration is probably close to zero over
the course of a year so I took the liberty of assuming it so. Maybe
that's the 2% error factor.

The acceleration due to the Sun fell from
3.69*10^-6 m/s^2 to 1.64*10^-6^2 m/s over
the period from the beginning of 1987 to
the end of 1994. During that time the
anomaly consisted of an additional constant
acceleration of 8.74*10^-10 m/s^2.

In any event The Times takes pains to be
accurate and they were dealing directly with the discoverer of the
anomaly at JPL so I'm confindent they got their figures from him all
the while acknowledging the figures as approximate.


I too have discussed the anomaly with one
of the authors and Craig Markwardt repeated
the calculations using different software
and got the same result. His paper is he

http://www.arxiv.org/abs/gr-qc/0208046

I get a mention in the acknowledgements
so I know what I'm talking about too.

The speed of the craft fell from 7.98 miles/sec to
7.71 miles/sec over the period while the anomaly
increased linearly from 0 to about 100 mm/s in the
same period (I'm not going to turn 100 mm/s into
miles per second!)

Well here I can only fall back on the numbers in the article. I just
checked them and they were an expectation D of 219 million miles of
travel in a particular year, a discrepancy d of 8,000 miles in the
same year which translate into ratios of d/D=v/c to within 2%. That's
all I ever intended by "calculating the Pioneer anomaly". It was just
showing the source of the anomaly in mechanical terms. I wouldn't
expect the same anomaly would have been present throughout the journey
but apparently it was during composition of the article. You are
welcome to check the article and the numbers of course.

I guess you mean this

http://tinyurl.com/rfotm

the full article costs and I'm not paying
when I can get the original article for free.

I just calculated the expected discrepancy in
distance for 2004 and it's about 9000 miles
so not far off.

Expressing the effect
as a function of acceleration and the gravitational constant lies
outside my interest because the mechanical principle of interest is
gravitational doppler. The fact is that gravitational "constants" are
actually not constant at all and vary considerably in magnitude and
direction according to ordinary linear doppler effects of speed in
relation to the speed of light.

That's why I delayed calculation of the effect for a year. Everyone
appeared to be looking at a discrepancy in the gravitational constant
for explanation of the effect when it really has nothing to do with
that. It's just the doppler principle applied to gravitation in purely
mechanical terms of speed in relation to the speed of light.
Straightforward Newtonian gravitation adjusted for latency of
propagation.

"Latency of propagation" gives an entirely different
result. I get latency values of 2.1 to 7.2s over the
same period. Perhaps you could explain how you get
from latency to the speed related value.

Well I'm not sure what you mean by latency values here, George.

If there is a delay due to propagation then the
acceleration felt by the craft would be GM/r^2
but for r at a slightly earlier time. The anomaly
is a_P so the total acceleration is:

a = GM/r^2 + a_P

Let R be a reduced radius such that:

a = GM/r^2 + a_P = GM/R^2

then the latency time is the time it took for the
effect of gravity to get from R where the value
was produced to r where the craft had reached when
it was affected. The latency as a time t_lat is then:

t_lat = (r - R) / v

The numbers as I said range from about 2 to 7 seconds.

What I
have always meant by the term "latency" is taking into account the
latency of propagation associated with gravitation in relation to the
velocity of objects affected by gravitation as well as the effect of
rotational dynamics of bodies such as the sun and its impact on its
eccentric locus of gravitational attraction. So I don't quite know how
to give you any specific latency numbers except as v/c fractions of
velocity in relation to c at any given point in a trajectory.

You can see my method above.


--:--


"Lester Zick" wrote in message
news
On 24 Jul 2006 13:51:41 -0700, wrote:
Sci astro added, sci.math and comp.ai.p.. removed.
Lester Zick wrote:
On 24 Jul 2006 09:11:21 -0700, wrote:
....
At the time of publication
Pioneer was traveling about 7 miles/sec (actually 6.9444 . . .
according to my calculation.

In January 1987 the speed was 7.984026 mile/sec
In December 1994 the speed was 7.706486 mile/sec

Interesting. The article was dated 12/21/04 so my calculation of v
seems right in line.

It was about 7.529 miles/sec in the middle of 2004.

That number in relation to the speed of
light produces a ratio around 27,000

The ratios above are 23332 and 24172 respectively so
that's not bad given that you are using approximate
speeds.

Yeah. But I think you have to realize that I wasn't using speeds
directly as there were no speeds indicated in the article (alas!). All
I had to go on were the yearly expectation of distance D for some year
and the yearly discrepancy d presumably for the same year.

OK, that was reasonable given what you had to
go on. Hopefully the full paper above will
give you a much better picture. Unfortunately
what you couldn't know was that the quoted
discrepancy is only valid for that year.

....
Now that's where we diverge. What do you mean
by "the discrepancy in expected yearly distance
of travel"?

That's roughly the way the numbers were described in the article. As
noted just above I didn't use velocity numbers directly but expected
distance D and discrepancy in distance d in one year's travel because
that's what the article gave.

The anomaly is a constant acceleration
so the discrepancy is speed increases each year
and the discrepancy in distance is quadratic.

Disagree. Especially at distances where little or no significant
acceleration occurs.

Statement of fact, sorry, the Times article obviously
didn't make that clear.

snip background

Imagine for a moment that the locus of attraction in the solar system
suddenly moves. Do you imagine that planetary orbits would be
unaffected?

Changes in gravity are expected to propagate at c.

Of course. And I have no doubt the basic force itself does too. At
least that's what I would infer from my calculation of the Pioneer
anomaly as well as the idea that gravitation propagates in waves.

If the sun suddenly moved away from the earth the earth
would be tugged toward it by an amount linearly related to the speed
of movement of the sun and having nothing to do with gravitational
constants.

No, it would be unaffected for about 500s then the
force would start to diminish. I don't think you are
talking of gravito-magnetic effects which would be
very small if they existed in that configuration.

Well of course there is the propagation delay to consider but the
effect itself would still occur. But whether you're talking attraction
increase or decrease would depend on the direction of motion.

OK, that should give a bit of background to
why I calculated your "latency" they way I
did. It's not well thought out but was the
only way I could imagine to approach your
use of the term as "latency" normally means
a time delay.

Now in approaching the Pioneer anomaly all I did was show that the
ratio between distance of expected travel and discrepancy in expected
travel were almost identical (witnin 2%) of the speed of travel and
the speed of light. I extrapolated the magnitudes over a year to
conserve precision. In other words if we call the expected distance of
travel D and the discrepancy in expected travel d, the speed of travel
v and the speed of light c we find that D/d is almost exactly c/v.

The problem there is that the discrepancy is a constant
acceleration a_P hence

d = 1/2 * a_P * t^2

And I strongly (but politely) disagree because the anomaly is between
actual distance traveled versus expected distance traveled. Everything
else represents potential assumptions and interpretations used to
explain the source of discrepancy but the actual discrepancy itself is
actual distance traveled versus expected distance traveled.

No, what is measured for Pioneer is the frequency
of the telemetry carrier. Doppler on that gives a
speed and there is an error in the speed versus the
best fit model which increases linearly with time.
Look at Figure 8 on page 20 of the Anderson paper.

http://www.arxiv.org/abs/gr-qc/0104064

while the speed is almost constant so

D ~ v * t

then

D/d ~ (2 * v) / (a_P * t)

snip Mercury

I hope this explanation is a little clearer.

Yes, it is better and hopefully my consternation is
a little clearer too. v/c is constant and D increases
linearly with time whereas d increases with the
square of time because it is a constant acceleration.

In the absence of significant acceleration v/c is constant and both D
and d are linear functions of time and constant over one year periods.

Unfortunately the anomaly itself is a constant
acceleration and about 3000 times smaller than
the gravitational acceleration of the Sun. That
said, even the latter is so small it only changed
the craft speed by 3.5% in 8 years so you can take
the speed as being almost constant but you then
have to process accelerations.

I was trying to understand your description and guessed
badly. You said the extra force was related to the speed
ratio and since that is dimensionless you need to multiply
it by an acceleration or speed to get it into dynamical units.

Well you know I'd like to stay away from the term "force" in the
present context because I can't describe how this force translates
into a constant change in velocity at present.

Easy, the anomaly is a constant acceleration a_P. The
force is simply a_P / M and the mass of the craft is
discussed in the paper, round about 241 kg. As for
translation:

constant acceleration == linear change of speed

though the discovery process uses that the other way
round.

All I can actually
claim is to have calculated a constant ratio v/c reflective of the
anomaly to within 2% and speculate it is a linear doppler ratio
indicating a relative lenghening in gravitational wavelenghts.

The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.

I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

All I have right now is a linear ratio v/c which correlates with the
Pioneer anomaly almost exactly. The ratio almost certainly reflects a
first order doppler effect in terms of the propagation of gravitation
but exactly how this ratio translates into a constant change in v is
not apparent at least to me. Perhaps there are others more familiar
with longitudinal doppler effects who could comment. However it is
enough for the present that we can calculate the effect directly. As
noted in a collateral post I never suggested I can calculate variances
in gravitational constants directly as a function of velocity. But I'm
convinced the effect itself is real and the calculations reflect that.

Unfortunately your value only matches for that one
year, for the year 1987 the discrepancy d was only
about 245 miles. It is a strange coincidence but
there are a lot of those in this topic. No doubt
you will come across more if you continue to study
the anomaly, but please at least skim Anderson's
paper first, you will save yourself a lot of effort.
If you can read that and Markwardt's paper in more
detail you will find them fascinating insights into
how the data was processed and how much has been
ruled out.

George

wrote:
Sci astro added, sci.math and comp.ai.p.. removed.


Lester Zick wrote:

On 24 Jul 2006 09:11:21 -0700, wrote:


Lester Zick wrote:

Gravitational Doppler
~v~~

We are well aware of gravitational lensing but there is another EM
analog associated with Newtonian universal gravitation as well:
gravitational doppler. In other words with latency extensions to
Newtonian universal gravitation we can explain planetary orbital
perihelion anomalies and calculate the Pioneer anomaly in simple,
direct terms.

To do this we only need to calculate Pioneer's velocity away from the
sun as a fraction of the speed of light and recognize that the effect
of the sun's gravitation will increase in proportion:

(Numbers used here were drawn from a column 1 article in the L. A.
Times of 12/21/2004 and are not exact)

Yearly distance traveled by Pioneer = 219,000,000 miles

Yearly discrepancy in distance = 8,000 miles

Ratio = ~ 27,375

speed of light = 186,289 miles per
second

Yearly distance traveled by light in one year=

186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr

Divided by yearly distance traveled by Pioneer

Ratio = ~ 26,825

A difference between the two ratios of 2% (27375 - 26,825 / 27,375)

QED

~v~~

I can't see any relation between the calculation above
and the description below.

Perhaps it wasn't as clear as I had hoped.


I made an error in my calculation, I used km/s
in one place and m/s in another, doh! That
knocks a factor of 1000 out in the results so
our numbers are much closer, sorry.


At the time of publication
Pioneer was traveling about 7 miles/sec (actually 6.9444 . . .
according to my calculation.


In January 1987 the speed was 7.984026 mile/sec
In December 1994 the speed was 7.706486 mile/sec


That number in relation to the speed of
light produces a ratio around 27,000


The ratios above are 23332 and 24172 respectively so
that's not bad given that you are using approximate
speeds.


or within 2% of the discrepancy
in distance traveled. In other words the discrepancy in expected
yearly distance of travel would be proportional to the ratio between
the speed of travel and the speed of light taken as the speed of
propagation for gravity.


Now that's where we diverge. What do you mean
by "the discrepancy in expected yearly distance
of travel"? The anomaly is a constant acceleration
so the discrepancy is speed increases each year
and the discrepancy in distance is quadratic.


Ordinarily we consider doppler primarily in terms of repulsive forces,
radiation, sound, etc.


No, ordinarily we think of Doppler as a change of
frequency and not related to forces. Light is an
exception since radiation pressure depends on
frequency, but that's not too significant at the
moment


However doppler also operates in analogous
terms for attractive forces such as gravitation, electrostatic, and
magnetic forces except that effects are reversed.

Consider two strong magnets on a table. They remain stationary as long
as first order friction effects exceed magnetic attraction between
them. However if one magnet is dragged away from the other at high
speed the other magnet experiences an excess force of attraction
causing it to move toward the moving magnet.


Really? I haven't worked out the details but I
haven't seen that effect. I suppose it might
result from induction.


The effect is pure doppler except in the case of attractive forces an
increase in speed away increases wavelengths and strength of the
attractive force. The same is true of all attractive forces operating
through space. Increasing wavelengths of attractive forces increases
the degree of attraction and decreasing wavelengths of attractive
forces decreases attraction by amounts proportional to increases or
decreases of speed in relation to the speed of propagation for the
force, the speed of light.

Imagine for a moment that the locus of attraction in the solar system
suddenly moves. Do you imagine that planetary orbits would be
unaffected?


Changes in gravity are expected to propagate at c.


If the sun suddenly moved away from the earth the earth
would be tugged toward it by an amount linearly related to the speed
of movement of the sun and having nothing to do with gravitational
constants.


No, it would be unaffected for about 500s then the
force would start to diminish. I don't think you are
talking of gravito-magnetic effects which would be
very small if they existed in that configuration.


And conversely if the sun suddenly moved toward the earth
its attraction would be lessened by a comparable amount and the orbit
of the earth extended as a result.

Now in approaching the Pioneer anomaly all I did was show that the
ratio between distance of expected travel and discrepancy in expected
travel were almost identical (witnin 2%) of the speed of travel and
the speed of light. I extrapolated the magnitudes over a year to
conserve precision. In other words if we call the expected distance of
travel D and the discrepancy in expected travel d, the speed of travel
v and the speed of light c we find that D/d is almost exactly c/v.


The problem there is that the discrepancy is a constant
acceleration a_P hence

d = 1/2 * a_P * t^2

while the speed is almost constant so

D ~ v * t

then

D/d ~ (2 * v) / (a_P * t)

snip Mercury

I hope this explanation is a little clearer.


Yes, it is better and hopefully my consternation is
a little clearer too. v/c is constant and D increases
linearly with time whereas d increases with the
square of time because it is a constant acceleration.


In other words Pioneer travels about 7 miles per second away from the
sun and in doing so gravitation waves lengthen and their attractive
intensity is experienced longer in each wave. (In this respect unlike
repulsive waves like EM radiation, the effect of attraction increases
in gravitation with longer waves and decreases with shorter waves.)
And conversely the attraction of gravitation should decrease as the
sun is approached.

If it is increased when the craft is moving away from
the Sun and decreased when moving towards, it is
first order and the Sun's gravitational effect would be
changed from

a = GM/r^2

to

a' = (1+v/c) * GM/r^2

The discrepancy would be

a_P = v/c * GM/r^2

For Pioneer 10 that varies from 1.58*10^-13 m/s^2 at
40AU down to 6.77*10^-14 m/s^2 at 60AU. The anomaly
is actually 8.74*10^-10 m/s^2 so your prediction is too
small by a factor of about 5000 at the start and more than
double that by the end of the period they studied. Your


Clearly the Pioneer Anomaly is caused by what I call gravitational
doppler. ....

Not even close.

Well, George, I'm not sure what the problem is here.


Most of it was mine.


I show the
expected discrepancy in distance traveled by Pioneer is proportional
to c/v and you tell me it isn't because you insist on relating it to
gravitational acceleration instead of the actual anomaly. The
discrepancy is in net distance traveled versus expected distance
traveled and not in gravitational acceleration.


I was trying to understand your description and guessed
badly. You said the extra force was related to the speed
ratio and since that is dimensionless you need to multiply
it by an acceleration or speed to get it into dynamical units.


The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.


I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

George


Given that

c/D = v/d

Will

d c = D v = Constant

do it?

d is quadratic
D is linear
v is linear

Richard

On Tue, 25 Jul 2006 10:42:09 +0100, "George Dishman"
wrote:

I'll coalesce my replies:

George, for what it's worth in the past as these post/reply sequences
lengthen I've found the reverse approach more useful, that is not to
coalesce replies but to reply more or less in pieces to decrease the
turnaround time for individual pieces. For my part since we're just
conversing here I'd like to use that practice at least until we reach
some consensus on what we're talking about.

"Lester Zick" wrote in message
.. .
On Mon, 24 Jul 2006 22:38:04 +0100, "George Dishman"
wrote:
"Lester Zick" wrote in message
...
On 24 Jul 2006 05:20:36 -0700, wrote:
...

Lester, the original Anderson paper is he

http://www.arxiv.org/abs/gr-qc/0104064

That's the abstract, there should be a PDF option
on the page that gives you the full document (I have
some preferences set so I get PDF by default, it
might be an option for you).

I've downloaded the pdf and am studying it. I won't try to comment in
the interim except to minor unrelated stuff. So it'll be several hours
to a day or more before I can comment further on the main topic.

[. . .]

Lester Zick
~v~~

On Tue, 25 Jul 2006 10:42:09 +0100, "George Dishman"
wrote:

I'll coalesce my replies:


"Lester Zick" wrote in message
.. .
On Mon, 24 Jul 2006 22:38:04 +0100, "George Dishman"
wrote:
"Lester Zick" wrote in message
...
On 24 Jul 2006 05:20:36 -0700, wrote:
...

Lester, the original Anderson paper is he

http://www.arxiv.org/abs/gr-qc/0104064

That's the abstract, there should be a PDF option
on the page that gives you the full document (I have
some preferences set so I get PDF by default, it
might be an option for you).

George, I appreciate the original reference but after several hours
reviewing it am having considerable difficult finding out exactly
where and how the acceleration was measured. I see numerous references
to variances in acceleration and about everything else under the sun
but nothing that shows what measured acceleration. For instance was it
an accelerometer of some kind? Or was the measure of acceleration
simply inferred from some other measurement? If you could tell me or
at least point me to a page reference in the document it would be much
appreciated. I'll try to reply to the balance of this post tomorrow.
Thanks.

Lester Zick
~v~~

Lester Zick wrote:
On Tue, 25 Jul 2006 10:42:09 +0100, "George Dishman"
wrote:

I'll coalesce my replies:


"Lester Zick" wrote in message
.. .
On Mon, 24 Jul 2006 22:38:04 +0100, "George Dishman"
wrote:
"Lester Zick" wrote in message
...
On 24 Jul 2006 05:20:36 -0700, wrote:
...

Lester, the original Anderson paper is he

http://www.arxiv.org/abs/gr-qc/0104064

That's the abstract, there should be a PDF option
on the page that gives you the full document (I have
some preferences set so I get PDF by default, it
might be an option for you).

George, I appreciate the original reference but after several hours
reviewing it am having considerable difficult finding out exactly
where and how the acceleration was measured.

There is a lot in the paper.

The basic technique is that a signal was sent to
the craft, the uplink. When that was received, the
craft was configured to lock its return (downlink)
carrier to an exact multiple of the uplink frequency.
The frequencies of the uplink and downlink were
measured and recorded. The difference is the
Doppler shift which indicates relative speed.

The component due to the motion of the Earth
is known and the remainder should indicate the
motion of the craft.

A 'best fit' of the craft motion to the measured
Doppler is then produced using an optimum
initial velocity and the known gravitational
acceleration of all major solar system bodies.
The Doppler due to that motion is then predicted.
In theory of course it should be a perfect match
to what was received since the trajectory was
fitted to the data but it doesn't quite work. The
reminder is plotted in Figure 8 and shows an
apparent linearly increasing discrepancy in the
velocity of the craft compared to that modelled,
i.e. a constant acceleration.

I see numerous references
to variances in acceleration and about everything else under the sun
but nothing that shows what measured acceleration. For instance was it
an accelerometer of some kind? Or was the measure of acceleration
simply inferred from some other measurement? If you could tell me or
at least point me to a page reference in the document it would be much
appreciated.

Section II, D on page 5 gives a description of the
overall communications system, Section III, A on
page 8 describes the measurement equipment
and Section III, B, 1 on page 9 explains the
method. This gives speed and acceleration is
inferred as explained above.

Unfortunately, direct range measurement wasn't
available from Pioneer 10 due to problems with
the craft losing lock when it was attempted.

George

Richard Saam wrote:
wrote:
Lester Zick wrote:
....
The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.


I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

Given that

c/D = v/d

Will

d c = D v = Constant

do it?

d is quadratic
D is linear
v is linear

No, v is nearly constant. c/D ~ v/d is only
approximately true in one particular year.

George

On Tue, 25 Jul 2006 16:32:49 GMT, Richard Saam wrote:

wrote:
Sci astro added, sci.math and comp.ai.p.. removed.


Lester Zick wrote:

On 24 Jul 2006 09:11:21 -0700, wrote:


Lester Zick wrote:

Gravitational Doppler
~v~~

We are well aware of gravitational lensing but there is another EM
analog associated with Newtonian universal gravitation as well:
gravitational doppler. In other words with latency extensions to
Newtonian universal gravitation we can explain planetary orbital
perihelion anomalies and calculate the Pioneer anomaly in simple,
direct terms.

To do this we only need to calculate Pioneer's velocity away from the
sun as a fraction of the speed of light and recognize that the effect
of the sun's gravitation will increase in proportion:

(Numbers used here were drawn from a column 1 article in the L. A.
Times of 12/21/2004 and are not exact)

Yearly distance traveled by Pioneer = 219,000,000 miles

Yearly discrepancy in distance = 8,000 miles

Ratio = ~ 27,375

speed of light = 186,289 miles per
second

Yearly distance traveled by light in one year=

186,289 mi/sec x 1440 min/day x 60 sec/min x 365 days/yr

Divided by yearly distance traveled by Pioneer

Ratio = ~ 26,825

A difference between the two ratios of 2% (27375 - 26,825 / 27,375)

QED

~v~~

I can't see any relation between the calculation above
and the description below.

Perhaps it wasn't as clear as I had hoped.


I made an error in my calculation, I used km/s
in one place and m/s in another, doh! That
knocks a factor of 1000 out in the results so
our numbers are much closer, sorry.


At the time of publication
Pioneer was traveling about 7 miles/sec (actually 6.9444 . . .
according to my calculation.


In January 1987 the speed was 7.984026 mile/sec
In December 1994 the speed was 7.706486 mile/sec


That number in relation to the speed of
light produces a ratio around 27,000


The ratios above are 23332 and 24172 respectively so
that's not bad given that you are using approximate
speeds.


or within 2% of the discrepancy
in distance traveled. In other words the discrepancy in expected
yearly distance of travel would be proportional to the ratio between
the speed of travel and the speed of light taken as the speed of
propagation for gravity.


Now that's where we diverge. What do you mean
by "the discrepancy in expected yearly distance
of travel"? The anomaly is a constant acceleration
so the discrepancy is speed increases each year
and the discrepancy in distance is quadratic.


Ordinarily we consider doppler primarily in terms of repulsive forces,
radiation, sound, etc.


No, ordinarily we think of Doppler as a change of
frequency and not related to forces. Light is an
exception since radiation pressure depends on
frequency, but that's not too significant at the
moment


However doppler also operates in analogous
terms for attractive forces such as gravitation, electrostatic, and
magnetic forces except that effects are reversed.

Consider two strong magnets on a table. They remain stationary as long
as first order friction effects exceed magnetic attraction between
them. However if one magnet is dragged away from the other at high
speed the other magnet experiences an excess force of attraction
causing it to move toward the moving magnet.


Really? I haven't worked out the details but I
haven't seen that effect. I suppose it might
result from induction.


The effect is pure doppler except in the case of attractive forces an
increase in speed away increases wavelengths and strength of the
attractive force. The same is true of all attractive forces operating
through space. Increasing wavelengths of attractive forces increases
the degree of attraction and decreasing wavelengths of attractive
forces decreases attraction by amounts proportional to increases or
decreases of speed in relation to the speed of propagation for the
force, the speed of light.

Imagine for a moment that the locus of attraction in the solar system
suddenly moves. Do you imagine that planetary orbits would be
unaffected?


Changes in gravity are expected to propagate at c.


If the sun suddenly moved away from the earth the earth
would be tugged toward it by an amount linearly related to the speed
of movement of the sun and having nothing to do with gravitational
constants.


No, it would be unaffected for about 500s then the
force would start to diminish. I don't think you are
talking of gravito-magnetic effects which would be
very small if they existed in that configuration.


And conversely if the sun suddenly moved toward the earth
its attraction would be lessened by a comparable amount and the orbit
of the earth extended as a result.

Now in approaching the Pioneer anomaly all I did was show that the
ratio between distance of expected travel and discrepancy in expected
travel were almost identical (witnin 2%) of the speed of travel and
the speed of light. I extrapolated the magnitudes over a year to
conserve precision. In other words if we call the expected distance of
travel D and the discrepancy in expected travel d, the speed of travel
v and the speed of light c we find that D/d is almost exactly c/v.


The problem there is that the discrepancy is a constant
acceleration a_P hence

d = 1/2 * a_P * t^2

while the speed is almost constant so

D ~ v * t

then

D/d ~ (2 * v) / (a_P * t)

snip Mercury

I hope this explanation is a little clearer.


Yes, it is better and hopefully my consternation is
a little clearer too. v/c is constant and D increases
linearly with time whereas d increases with the
square of time because it is a constant acceleration.


In other words Pioneer travels about 7 miles per second away from the
sun and in doing so gravitation waves lengthen and their attractive
intensity is experienced longer in each wave. (In this respect unlike
repulsive waves like EM radiation, the effect of attraction increases
in gravitation with longer waves and decreases with shorter waves.)
And conversely the attraction of gravitation should decrease as the
sun is approached.

If it is increased when the craft is moving away from
the Sun and decreased when moving towards, it is
first order and the Sun's gravitational effect would be
changed from

a = GM/r^2

to

a' = (1+v/c) * GM/r^2

The discrepancy would be

a_P = v/c * GM/r^2

For Pioneer 10 that varies from 1.58*10^-13 m/s^2 at
40AU down to 6.77*10^-14 m/s^2 at 60AU. The anomaly
is actually 8.74*10^-10 m/s^2 so your prediction is too
small by a factor of about 5000 at the start and more than
double that by the end of the period they studied. Your


Clearly the Pioneer Anomaly is caused by what I call gravitational
doppler. ....

Not even close.

Well, George, I'm not sure what the problem is here.


Most of it was mine.


I show the
expected discrepancy in distance traveled by Pioneer is proportional
to c/v and you tell me it isn't because you insist on relating it to
gravitational acceleration instead of the actual anomaly. The
discrepancy is in net distance traveled versus expected distance
traveled and not in gravitational acceleration.


I was trying to understand your description and guessed
badly. You said the extra force was related to the speed
ratio and since that is dimensionless you need to multiply
it by an acceleration or speed to get it into dynamical units.


The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.


I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

George


Given that

c/D = v/d

Will

d c = D v = Constant

do it?

d is quadratic
D is linear
v is linear

My calculation doesn't use c or v directly. It uses D/d cited in the
article and c*186289*1440*60*365/D. The result is accurate to 2%.
These D and d values were rough approximations and subject to change
over time but are assumed accurate in relation to each other for the
period cited.

Lester Zick
~v~~

On 26 Jul 2006 02:18:05 -0700, "George Dishman"
wrote:


Richard Saam wrote:
wrote:
Lester Zick wrote:
...
The calculation is
correct for the numbers given within the stated limits of precision.
If you wish to relate the effect of gravitational doppler to actual
gravitational acceleration you really have to take the basic
calculation of the anomaly c/v and retrofit it to accommodate the
correctness of that calculation.


I'm not sure what you mean by that but the key
question is how you relate the constant value of
v/c and the linearly increasing D to the quadratic
discrepancy d.

Given that

c/D = v/d

Will

d c = D v = Constant

do it?

d is quadratic
D is linear
v is linear

No, v is nearly constant. c/D ~ v/d is only
approximately true in one particular year.

Disagree. The ratios themselves vary individually but their
relationship to each other remains constant. It's how the effect is
mechanized to begin with. More precisely the ratio v/c is what governs
gravitational doppler and what causes the anomalous acceleration in
Pioneer.

Lester Zick
~v~~